The present invention relates to methods of measuring pneumatic tire uniformity and, more particularly, to methods of predicting high-speed tire uniformity.
In the art of manufacturing pneumatic tires, rubber flow in the tire mold or minor differences in the dimensions of the belts, beads, liners, treads, plies of rubberized cords, etc., sometimes cause non-uniformities in the final tire. Non-uniformities of sufficient amplitude will cause force variations on a surface, such as a road, against which the tires roll producing vibration and noise. When such force variations exceed an acceptable maximum level, the ride and handling of a vehicle utilizing such tires will be adversely affected. It is known that the magnitudes of the force variations change with the speed of tire rotation, generally (but not always) increasing in magnitude with speed, therefore a vehicle operator""s perception of tire quality (and vehicle ride) will be most influenced by the force variations occurring at high speeds such as xe2x80x9chighway speedsxe2x80x9d of, for example, 100 kilometers per hour (kph) and higher. Accordingly, purchasers of tires, especially large volume purchasers such as vehicle manufacturers (xe2x80x9cOEMsxe2x80x9d), would prefer to know and specify maximums for high speed force variations on purchased tires. Unfortunately, direct measurement of high speed force variations on all tires is difficult and expensive, therefore the industry has devised a variety of equipment and methods for predicting high speed tire performance (uniformity, force variations) based on statistical sampling and on simpler measurements primarily including xe2x80x9clow speedxe2x80x9d tire uniformity measurements, and possibly also measurements of tire balance.
During the typical tire manufacturing process, factory floor measurements of tire uniformity are performed on tire uniformity machines (xe2x80x9cTUMsxe2x80x9d), which are used to monitor the quality of the tire production process and may guide or incorporate corrective measures such as grinding to improve the balance and uniformity of a tire. A factory floor TUM is a low speed unit, typically operated at 60 revolutions per minute (rpm), which corresponds to less than 10 kph for a typical passenger car tire. In general, a tire uniformity machine subjects a tire to normal conditions of mounting, inflation, load, and rotation (at low speed) while collecting measurement data on variations of force, and sometimes also deflection (e.g., xe2x80x9crunoutxe2x80x9d), and instantaneous angular velocity. A tire uniformity machine typically includes an assembly for rotating a test tire against the surface of a freely rotating load wheel. In such an arrangement, the load wheel is acted upon in a manner dependent on the forces exerted by the rotating tire, which are measured by appropriately placed measuring devices connected to the supporting structure of the loading wheel. When a tire being tested yields unacceptable results, shoulder and center rib grinders are used to remove a small amount of the tire tread at precisely the location of non-uniformities detected by the measuring devices. As the tire is rotated, it is measured and ground simultaneously. In a sophisticated, low speed production tire uniformity machine, such as a Model No. D70LTX available from the Akron Standard Co. of Akron Ohio, the force measurements are interpreted by a computer and rubber is removed from the tire tread using grinders controlled by the computer.
Once a tire undergoes correction for force variations in a TUM, it is common manufacturing practice to remove the tire from the TUM and place the tire in a balance machine to measure the amount of imbalance of the tire. Typically, the tires are mounted in the balance machine in a manner similar to that of the tire uniformity machine and inflated to a preset pressure. Then, the static (single-plane) and couple (two-plane) imbalances are measured by one of a variety of well-known methods. When a tire is found to be imbalanced to an unacceptable level, the tire is ordinarily scrapped.
The assumption generally made in the art is that the factory floor measurements of tire quality are reasonably related to high speed tire performance, so that placing xe2x80x9csuitablexe2x80x9d limits on tire imbalance and on low speed force variations will produce tires that have acceptable high speed performance. A common technique for establishing the suitable limits is to measure individual tires at both high speed and low speed and then mathematically relate the two measurements. In this technique""s simplest conceptual form, a tire is found that exhibits the maximum allowable high speed force variation, and then the magnitude of the low speed force variation measured for the same tire is used as the suitable limit. It is known that the relationship between high speed force variation and low speed force variation can be different for different tire constructions (designs) and for different low and high speed tire uniformity machines, so this technique must be repeated for each variation of tire and machine. In many cases, it is desired to be able to predict the magnitude of high speed force variations from factory floor measurements, and so inventive effort, detailed hereinbelow, has been applied to the determination of mathematical equations (including xe2x80x9ctransfer functionsxe2x80x9d) to relate various combinations of factory floor measurements to predicted high speed force variations.
Before discussing transfer functions and prediction methods, it is important to understand the various measurements that are involved. Tire performance, in terms of vibration (and noise caused by tire vibration) at any given tire rotational speed, is substantially determined by tire uniformity and is directly indicated by the magnitude of force variations, which occur as the tire rolls under load on a surface. If the surface is a tire uniformity machine load wheel that is instrumented to measure forces, then the forces can be measured to report a direct measurement of the tire""s vibration performance (i.e., uniformity) for the tire speed at which it is measured. Since high speed tire uniformity measurements are impractical for large volume factory floor use, low speed TUM measurements must be utilized to predict high speed measurements. The problem is that with low speed TUMs, certain force variations are either too small to be accurately measured at low speeds, or else a measurement of a particular low speed force variation is not sufficient to predict the high speed variation of that force. For these certain force variations, low speed force measurements must be supplemented or replaced with other measurements including, for example, measurements of: other types of force variation, tire imbalance, tire surface displacement (runout), tire stiffness variation, tire angular velocity variation and load wheel velocity variation.
In the art, forces of a tire that is rolling under load on a load bearing surface are commonly broken down into three orthogonal components which will be primarily referred to herein as: radial, lateral, and tangential. Radial forces act in the tire""s radial direction, i.e., perpendicular to the tire""s axis of rotation. Radial forces are strongest in the vertical direction (e.g., tire xe2x80x9chopxe2x80x9d) as the tire interacts with the load bearing surface, but may also have a horizontal (fore-aft, or xe2x80x9csurgexe2x80x9d) component due to, for example, the radial centrifugal force of a net mass imbalance in the rotating tire. Lateral forces act in a direction parallel to the tire""s axis of rotation, and generally occur where the tire""s surface touches the load bearing surface. Lateral force causes either tire wobble or a constant steering force. Tangential force, or fore-aft force is experienced at the surface of contact between tire and load bearing surface in a direction both tangential to the tire""s outer circumference (e.g., tread surface) and perpendicular to the tire""s axis of rotation (thus also perpendicular to the radial and lateral forces). Tangential force variations are experienced as a xe2x80x9cpush-pullxe2x80x9d effect on a tire, which can be analogized to the sensation of a wheel barrow traveling over a bump in the road, i.e. increased force as the wheel barrow is pushed up the bump and decreased force as the wheel barrow travels down the bump. Investigations have shown that there are multiple mechanisms active in causing tangential force variation.
Of the three types of force (radial, tangential and lateral), tangential force variation (TFV) is the most speed dependent, and is practically immeasurable on a typical production low speed tire uniformity machine, which operates at a speed such as 60 rpm. Instead, tangential force variation can only be effectively measured at highway speeds using a high speed, laboratory tire uniformity machine, such as a Model HSU-1064, available from the Akron Standard Co. of Akron Ohio.
Variations of the three types of force are known to be caused by non-uniformities (asymmetries, imperfections) in the tire (and/or in the wheel and axle hub upon which the tire is mounted). Other sources of force, such as friction drag, are also known but are not a concern in this discussion of tire uniformity. Non-uniformities in the tires can be generally classified as asymmetries in mass, dimensional quantities and stiffness. A tire that is asymmetric from axial side to axial side may produce lateral forces, and asymmetry between angular points around the tire""s rotational axis will cause variations in force as the tire rotates. An imperfection that occurs only once around the tire, for example a single bump on the tire tread, may cause a strong force variation with a period which matches the period of the tire""s revolution, i.e., once per revolution when the bump hits the load bearing surface. Superimposed on the measurement of this strong force variation may be another force measured as the centrifugal force of the bump with a magnitude that will vary sinusoidally and have the same period as the tire revolution. A second bump on the tire tread would produce a second peak in a curve plotting the force measurements versus time. Obviously the force measurement curve can rapidly become quite complex. Through the well-known mathematical process of Fourier Transform calculation, even very complex periodic force variation measurement curves can be mathematically represented as a sum of components wherein each component is a sine curve characterized by its own amplitude and phase. The component of the Fourier equation, which has the same period as the tire revolution, i.e., has a frequency of one cycle per revolution of the tire, is referred to as the xe2x80x9cfirst harmonicxe2x80x9d. For example, if the tire is rotating at 60 revolutions per minute, then the first harmonic is a sine curve with a frequency of 60 cycles per minute (1 cycle per second, or 1 Hertz). The component of the Fourier equation that has half the period of the tire revolution (twice the revolution frequency) is the xe2x80x9csecond harmonicxe2x80x9d, and so on.
Since there are three orthogonal forces being considered, there are three separate force variation measurement curves: radial force variation (RFV), lateral force variation (LFV), and tangential force variation (TFV). Fourier transformations of each of the three force variation measurement curves will produce families of harmonic components (some of which may have a zero magnitude) for each of the three curves. The first harmonic of radial force variation can be abbreviated as xe2x80x9cR1Hxe2x80x9d for Radial 1st Harmonic; the first harmonic of lateral force variation can be abbreviated as xe2x80x9cT1Hxe2x80x9d for Lateral 1st Harmonic; and the first harmonic of tangential force variation can be abbreviated as xe2x80x9cT1Hxe2x80x9d for Tangential 1st Harmonic. Similarly, second harmonic components can be abbreviated as R2H, L2H, and T2H, for radial, lateral and tangential 2nd harmonics, respectively; and so on for third and higher harmonics of the three force variations.
As alluded to hereinabove, tire imbalance (mass asymmetry) is a contributing factor in certain tire force variation measurements. Tire imbalance can produce significant force variations, but fortunately is easily measured, even at relatively low tire revolution speeds (e.g., about 300 rpm), although tire balance measuring machines suitable for factory floor use are available which can be used with much higher rpm speeds than the factory floor TUMs.
Two separate physical phenomena can be used to model the imbalance of a tire, static imbalance and couple imbalance. Static imbalance is the net result of centrifugal forces created by non-uniformities in the distribution of tire mass (mass asymmetry) around the circumference of the tire. As an element of tire mass rotates about an axis, centrifugal force is experienced by the element, which tends to pull it away from the center of rotation (axis), the magnitude of this centrifugal force being:
F=mxc3x97xcfx892xc3x97r
wherein m=mass of the element, xcfx89=rotational velocity, and r=radius of the element""s location relative to the axis of rotation. If the mass of the tire is distributed equally about the center of rotation, the centrifugal force on each of the elements of tire mass would be negated by an equal and opposite force acting upon an element of tire mass located on the opposite side of the center of rotation, and thus no net centrifugal force would act upon the tire during rotation. However, when the distribution of tire mass is nonuniform, so that there are elements of differing mass opposing each other, or opposing elements of equal mass which are located at differing radial distances from the center of rotation, the centrifugal force on these elements is not canceled by the opposing force acting on the opposing element of tire mass located on the opposite side of the center of rotation. In such cases, the tire experiences a net force acting through the element of either greater tire mass or of equal mass located at a greater distance from the center of rotation. These net forces cause a static imbalance about the center of rotation of the tire. Static imbalance is also known as single plane imbalance, since the term is restricted to mass asymmetries that occur within a single circumferential plane of the tire (a plane perpendicular to the tire""s axis of rotation).
Couple imbalance is caused by the above described mass distribution non-uniformities, or mass imbalances/asymmetries, which occur in multiple circumferential planes, thereby creating net moments about an axis in a plane which is through the axial centerline of the tread and perpendicular to the axis of rotation of the tire. The magnitude of the moment equals the net force acting on the mass non-uniformity, or the imbalance force, multiplied by the axial distance of the mass non-uniformity from the centerline of the tread (and thus the axis located in the plane through the tread centerline). This moment M can be expressed as:
M=Fxc3x97d=(mxc3x97xcfx892xc3x97r)xc3x97d
wherein variables m, xcfx89, and r are the properties described above and d=axial distance between the mass non-uniformity and the centerline of the tread. The effect of such moments is that the tire tends to wobble, as the effective axis of rotation nutates. Couple imbalance is also referred to as xe2x80x9ctwo plane imbalancexe2x80x9d because the sum of all the couple imbalances in a tire can be resolved into a single net moment determined by two mass elements with a first element of mass m1 located at a certain angle and radius (xcfx861,r1) in a first circumferential plane located at a distance d1 from the centerline of the tread, and a second element of mass m2 located at a certain angle and radius xcfx862,r2) in a second circumferential plane located at a distance d2 from the centerline of the tread, such that d1=d2, m1=m2 and |xcfx861xe2x88x92xcfx862|=180xc2x0.
The combined effect of the static imbalance and the couple imbalance is referred to as the dynamic imbalance of a tire, which is the total imbalance experienced by a rotating tire. As static imbalance and couple imbalance are two distinct and mutually independent physical phenomena, the dynamic behavior of a rotating tire can be analyzed by overlaying the effect of static imbalance on the effect of couple imbalance. Virtually all tires have some differences in the distribution of the tire mass that causes dynamic imbalance to be present, but the imbalance will be negligible, or at least acceptable, in a xe2x80x9cuniformxe2x80x9d tire. Of course, as detailed hereinabove, measurement of uniformity and therefore acceptability of a tire is a rotational speed dependent phenomenon because the forces produced by non-uniformities are speed dependent.
U.S. Pat. No. 5,396,438(Oblizajek, assigned to General Motors Corporation, hereinafter referred to as the xe2x80x9cGM Patentxe2x80x9d), incorporated in its entirety by reference herein, discloses a method of manufacturing tires which preferably includes measurement of two or more low speed tire parameters, determination of transfer functions which are used to calculate predicted highway speed (high speed) force variations, and then comparison of high speed values predicted for production tires to predetermined criteria for controlling manufacture of the production tires responsive to the comparison. The determination of transfer functions comprises testing a sample set of tires at both low speed and high speed on tire uniformity machines. The GM Patent""s primary embodiment is for prediction of high speed, fore-aft (tangential) force variations (TFV), but it is stated that the method can be advantageously applied to prediction of high speed LFV and RFV in the same manner. It is further stated that any harmonic (xe2x80x9corder of tire rotationxe2x80x9d) of the high speed force variations can be predicted according to the disclosed method. The low speed measurements are made of two or more tire parameters selected from a list which includes: xe2x80x9cvariations in effective rolling radius, radial force variation, geometric runout variation, tread gauge variation of finished tire, variations in angles of internal tire reinforcing materials, that is, steel belts and fabric or steel body plies of the finished tire, variations in geometry, that is, widths and locations of edges and centerline of internal tire reinforcing materials such as steel belts and fabric or steel body plies of the finished tire, tread gauge variation of the tire at intermediate stages of manufacture, variations in angles of internal tire reinforcing materials, that is steel belts and fabric or steel body plies of the tire at intermediate stages of manufacture, variations in geometry, that is widths and locations of edges and the centerline of internal tire reinforcing materials such as steel belts and fabric or steel body plies at intermediate stages of manufacture and tire fore and aft force variation.xe2x80x9d (col. 15, line 63 et. seq.) In the claims, this list is generally narrowed to include xe2x80x9cselecting first and second measurable parameters from a set comprising: variation in effective rolling radius; radial force variation; geometric runout variation; and fore and aft force variation.xe2x80x9d The primary embodiment of the GM invention discloses an equation (6) in column 10 for a calculated prediction of the fore and aft force component Fxnm measured at the selected highway speed of tire xe2x80x98mxe2x80x99 at order (harmonic) xe2x80x98nxe2x80x99. The equation (6) is a sum of low speed measurements xe2x80x98Fxe2x80x99 multiplied by complex quantity transfer functions xe2x80x98Hxe2x80x99 for a tire xe2x80x98mxe2x80x99 at order (harmonic) xe2x80x98nxe2x80x99. Equation (6) uses the n,m components of three low speed measurements: Fznm is the radial force; Frnm is the effective rolling radius; and Funm is the geometric runout. An assumption that makes this equation usable is stated in col. 11, line 66 et. seq.: xe2x80x9cIf the quantities Hzn, Hrn, Hun, . . . are known, then Equation (6) can be used to predict Fxn. This has generally not been the case because the particular details and manner by which parameters such as tire mass, stiffness, and damping matrices or the equivalents, combine to effect the polynomials Pq(s) are unknown. However, as recognized by this invention, for quantities of tires manufactured by an individual tire manufacturer to a given engineering specification, i.e., where all tires are intended to be identical, these parameters will be relatively invariant among these ostensibly identical tires. Variations between tires, furthermore, will only occur in the measurements of non-uniformity, i.e., Fzn, Frn, Fun, . . . . xe2x80x9d
U.S. Pat. No. 6,065,331 (Fukasawa, assigned to Bridgestone Corporation, hereinafter referred to as the xe2x80x9cBridgestone Patentxe2x80x9d), incorporated in its entirety by reference herein, discloses method and apparatus for predicting a higher-order component 2nd and higher harmonics) of high speed uniformity of a tire, and method of manufacturing tires utilizing the method and apparatus. The method preferably comprises measuring, for a single tire within a tire lot, a low-speed dynamic stiffness at a frequency corresponding to an order of a higher-order component to be predicted when said tire rolls at a low speed, and a high-speed dynamic stiffness at a frequency corresponding to said order when said tire rolls at a high speed, and then using the dynamic stiffness measurements in an equation to predict high speed RFV or TFV from low speed measurements of RFV and radial runout (effective rolling radius). The preferred method of determining low speed radial runout is to calculate it from low speed TFV measurements, according to a linear relationship with slope and intercept constants determined by a linear regression calculation performed on measurements of 20 tires within the tire lot. The tire vertical dynamic stiffness is obtained from vertical displacement of a tire axis, namely, vertical displacement X of a drum surface, and vertical axial force Fz of a tire, which are measured by using a protrusion run-over type testing machine including a drum having a cleat mounted on the surface of the drum. The highest tire speed measured on such a drum is reported as 85 kph.
It is an object of the present invention to overcome perceived limitations in the methods of the GM Patent and of the Bridgestone Patent in order to improve and/or simplify the prediction of high speed tire uniformity for production tires using predictive calculations incorporating realistically achievable factory floor measurements of the production tires. Calculated prediction of all relevant harmonics of radial, lateral and tangential force variation for tire speeds in a wide range of high speeds is desired.
According to the invention, a method for predicting a harmonic component of force variation for a production tire comprises the steps of: collecting a set of measurement data for the production tire, the measurement data comprising measurements of the harmonic component of force variation at a plurality of intermediate test speeds on a factory floor tire uniformity machine; determining parameter values for a prediction equation by performing a curve fit of a predetermined curve type to the set of measurement data; and predicting a harmonic component of force variation for the production tire rotating at a prediction speed by applying the prediction speed to the prediction equation.
According to an aspect of the invention, the method is characterized by the step of predetermining an optimum quantity and individual values of the plurality of intermediate test speeds. Optionally, the steps of predetermining the curve type and the optimum quantity and individual values of the plurality of intermediate test speeds are accomplished by experimentation. Optionally, the steps of predetermining the curve type and the optimum quantity and individual values of the plurality of intermediate test speeds are performed for each tire construction, for each harmonic component to be predicted, and for each prediction speed. Preferably, the curve type is predetermined to be a parabolic curve type, and the quantity of the plurality of intermediate test speeds is predetermined to be at least three. Optionally, the method is further characterized by the steps of: predetermining a highest reasonable test speed and a lower test speed, which is less than the highest reasonable test speed; and spacing the individual values of the plurality of intermediate test speeds at approximately regular intervals between and including the lower test speed and the highest reasonable test speed. Preferably, the lower test speed is predetermined to be greater than 60 rpm, and most preferably to be at least 200 rpm. Optionally, the lower test speed is predetermined to be greater than 60 rpm, and at least 200 rpm below the highest reasonable test speed. Preferably, the lower test speed is predetermined to be approximately 300 rpm; and the highest reasonable test speed is predetermined to be approximately 750 rpm.
According to an aspect of the invention, the method is characterized by the step of performing the curve fit by means of a least squares curve fitting process. Optionally, the step of performing the curve fit comprises weighting higher speed measurement data points more than lower speed measurement data points.
According to the invention, a method of manufacturing tires comprises the steps of: collecting a set of measurement data for a production tire, the measurement data comprising measurements of a harmonic component of force variation at a plurality of intermediate test speeds on a factory floor tire uniformity machine; determining parameter values for a prediction equation by performing a curve fit of a predetermined curve type to the set of measurement data; predicting a harmonic component of force variation for the production tire rotating at a prediction speed by applying the prediction speed to the prediction equation; comparing the predicted harmonic component of force variation for the production tire to predetermined criteria; and controlling the manufacturing of production tires in response to results of the step of comparing.
According to an aspect of the invention, the method of manufacturing is characterized by the step of predetermining an optimum quantity and individual values of the plurality of intermediate test speeds. Optionally, the steps of predetermining the curve type and the optimum quantity and individual values of the plurality of intermediate test speeds are performed for each tire construction, for each harmonic component to be predicted, and for each prediction speed. Preferably, the curve type is predetermined to be a parabolic curve type, and the quantity of the plurality of intermediate test speeds is predetermined to be at least three. Optionally, the method of manufacturing is further characterized by the steps of: predetermining a highest reasonable test speed and a lower test speed which is less than the highest reasonable test speed; and spacing the individual values of the plurality of intermediate test speeds at approximately regular intervals between and including the lower test speed and the highest reasonable test speed.
According to the invention, an apparatus for controlling tire manufacturing comprises: factory floor testing equipment comprising an intermediate speed production tire uniformity machine for measuring production tires after a tire assembly process; a computer for collecting measurement data from the factory floor testing equipment, for curve fitting to determine prediction equation parameters, and for predicting a harmonic component of force variation; and a quality control means for accepting and rejecting production tires based on a harmonic component of force variation predicted for the production tires.
According to an aspect of the invention, the apparatus is characterized in that the quality control means provides feedback for correcting the tire assembly process.
According to another aspect of the invention, the apparatus is characterized in that the intermediate speed production tire uniformity machine is a low speed factory floor TUM, which has been modified for optimum performance when measuring each production tire at a plurality of intermediate speeds.
Other features and advantages of the invention will become apparent in light of the following description thereof.